Title: S-dual of Hamiltonian $\mathbf G$ spaces and relative Langlands duality Show Chinese title

Title: S对偶的哈密顿$\mathbf G$空间和相对朗兰兹对偶性

Abstract: The S-dual $(\mathbf G^\vee\curvearrowright\mathbf M^\vee)$ of the pair $(\mathbf G\curvearrowright\mathbf M)$ of a smooth affine algebraic symplectic manifold $\mathbf M$ with hamiltonian action of a complex reductive group $\mathbf G$ was introduced implicitly in [arXiv:1706.02112] and explicitly in [arXiv:1807.09038] under the cotangent type assumption. The definition was a modification of the definition of Coulomb branches of gauge theories in [arXiv:1601.03586]. It was motivated by the S-duality of boundary conditions of 4-dimensional $\mathcal N=4$ super Yang-Mills theory, studied by Gaiotto and Witten [arXiv:0807.3720]. It is also relevant to the relative Langlands duality proposed by Ben-Zvi, Sakellaridis and Venkatesh. In this article, we review the definition and properties of S-dual. Show Chinese abstract

Abstract: S对偶$(\mathbf G^\vee\curvearrowright\mathbf M^\vee)$的对$(\mathbf G\curvearrowright\mathbf M)$是一个光滑仿射代数辛流形$\mathbf M$在复半单群$\mathbf G$的哈密顿作用下，在余切类型假设下，隐式地在 [arXiv:1706.02112] 中提出，并在 [arXiv:1807.09038] 中显式地提出。该定义是对 [arXiv:1601.03586] 中规范理论的Coulomb分支定义的修改。它受到Gaiotto和Witten [arXiv:0807.3720] 研究的4维$\mathcal N=4$超Yang-Mills理论边界条件的S对偶性的启发。它也与Ben-Zvi、Sakellaridis和Venkatesh提出的相对Langlands对偶性有关。在本文中，我们回顾S对偶的定义和性质。